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An Introduction to Particle Accelerators

- Erik Adli, University of Oslo/CERN
- 2009
- Erik.Adli_at_cern.ch

v1.42 - short

LHC FIRST BEAM 10-sep-2008

Introduction

Part 1

Particle accelerators for HEP

- LHC the world biggest accelerator, both in

energy and size (as big as LEP) - Grand start-up and perfect functioning at

injection energy in September 2008 - First collisions expected in 2009

Particle accelerators for HEP

The next big thing. After LHC, a Linear Collider

of over 30 km length, will probably be needed

(why?)

Medical applications

- Therapy
- The last decades electron accelerators

(converted to X-ray via a target) are used very

successfully for cancer therapy) - Today's research proton accelerators instead

(hadron therapy) energy deposition can be

controlled better, but huge technical challenges - Imaging
- Isotope production for PET scanners

Advantages of proton / ion-therapy

( Slide borrowed from U. Amaldi )

Proton therapy accelerator centre

HIBAC in Chiba

What is all this? Follow the lectures... )

( Slide borrowed from U. Amaldi )

Synchrotron Light Sources

- the last two decades, enormous increase in the

use of synchrony radiation, emitted from particle

accelerators - Can produce very intense light (radiation), at a

wide range of frequencies (visible or not) - Useful in a wide range of scientific applications

Thorium - Accelerator Driven Systems

Basic concepts

Part 2

An accelerator

- Structures in which the particles will move
- Structures to accelerate the particles
- Structures to steer the particles

Lorentz equation

- The two main tasks of an accelerator
- Increase the particle energy
- Change the particle direction (follow a given

trajectory, focusing) - Lorentz equation
- FB ? v ? FB does no work on the particle
- Only FE can increase the particle energy
- FE or FB for deflection? v ? c ? Magnetic field

of 1 T (feasible) same bending power as en

electric field of 3?108 V/m (NOT feasible) - FB is by far the most effective in order to

change the particle direction

Acceleration techniques DC field

- The simplest acceleration method DC voltage
- Energy kick DEqV
- Can accelerate particles over many gaps

electrostatic accelerator - Problem breakdown voltage at 10MV
- DC field still used at start of injector chain

Acceleration techniques RF field

- Oscillating RF (radio-frequency) field
- Widerøe accelerator, after the pioneering work

of the Norwegian Rolf Widerøe (brother of the

aviator Viggo Widerøe) - Particle must sees the field only when the field

is in the accelerating direction - Requires the synchronism condition to hold

Tparticle ½TRF - Problem high power loss due to radiation

Acceleration techniques RF cavities

- Electromagnetic power is stored in a resonant

volume instead of being radiated - RF power feed into cavity, originating from RF

power generators, like Klystrons - RF power oscillating (from magnetic to electric

energy), at the desired frequency - RF cavities requires bunched beams (as opposed to

coasting beams) - particles located in bunches separated in space

From pill-box to real cavities

(from A. Chao)

LHC cavity module

ILC cavity

Why circular accelerators?

- Technological limit on the electrical field in an

RF cavity (breakdown) - Gives a limited ?E per distance
- ? Circular accelerators, in order to re-use the

same RF cavity - This requires a bending field FB in order to

follow a circular trajectory (later slide)

The synchrotron

- Acceleration is performed by RF cavities
- (Piecewise) circular motion is ensured by a guide

field FB - FB Bending magnets with a homogenous field
- In the arc section
- RF frequency must stay locked to the revolution

frequency of a particle (later slide) - Synchrotrons are used for most HEP experiments

(LHC, Tevatron, HERA, LEP, SPS, PS) as well as,

as the name tells, in Synchrotron Light Sources

(e.g. ESRF)

Digression other accelerator types

- Cyclotron
- constant B field
- constant RF field in the gap increases energy
- radius increases proportionally to energy
- limit relativistic energy, RF phase out of synch
- In some respects simpler than the synchrotron,
- and often used as medical accelerators
- Synchro-cyclotron
- Cyclotron with varying RF phase
- Betatron
- Acceleration induced by time-varying magnetic

field - The synchrotron will be the only circular

accelerator discussed in this course

Digression other accelerator types

- Linear accelerators for linear colliders
- - will be covered in lecture about linear

colliders at CERN

Particle motion

- We separate the particle motion into
- longitudinal motion motion tangential to the

reference trajectory along the accelerator

structure, us - transverse motion degrees of freedom orthogonal

to the reference trajectory, ux, uy - us, ux, uy are unit vector in a moving coordinate

system, following the particle

Longitudinal dynamicsfor a synchrotron

Part 3

Longitudinal Dynamics degrees of freedom

tangential to the reference trajectory us

tangential to the reference trajectory

RF acceleration

- We assume a cavity with an oscillating RF-field
- In this section we neglect the transit-transit

factor - we assume a field constant in time while the

particle passes the cavity - Work done on a particle inside cavity

Synchrotron with one cavity

- The energy kick of a particle, DE, depends on the

RF phase seen, f - We define a synchronous particle, s, which

always sees the same phase fs passing the cavity - ? wRF h wrs ( h harmonic number )
- E.g. at constant speed, a synchronous particle

circulating in the synchrotron, assuming no

losses in accelerator, will always see fs0

Non-synchronous particles

- A synchronous particle P1 sees a phase fs and get

a energy kick DEs - A particle N1 arriving early with f fs-d will

get a lower energy kick - A particle M1 arriving late with f fsd will get

a higher energy kick - Remember in a synchrotron we have bunches with a

huge number of particles, which will always have

a certain energy spread!

Frequency dependence on energy

- In order to see the effect of a too low/high DE,

we need to study the relation between the change

in energy and the change in the revolution

frequency (h "slip factor") - Two effects
- Higher energy ? higher speed (except

ultra-relativistic) - Higher energy ? larger orbit Momentum

compaction

Momentum compaction

- Increase in energy/mass will lead to a larger

orbit - We define the momentum compaction factor as
- a is a function of the transverse focusing in

the accelerator, altDxgt / R - ? a is a well defined quantity for a given

accelerator

Phase stability

- hgt0 velocity increase dominates, fr increases
- Synchronous particle stable for 0ºltfslt90º
- A particle N1 arriving early with f fs-d will

get a lower energy kick, and arrive relatively

later next pass - A particle M1 arriving late with f fsd will get

a higher energy kick, and arrive relatively

earlier next pass - hlt0 stability for 90ºltfslt180º
- h0 at the transition energy. When the

synchrotron reaches this energy, the RF phase

needs to be switched rapidly from fs to 180-fs

Transverse dynamics

Part 4

Transverse dynamics degrees of freedom

orthogonal to the reference trajectory ux the

horizontal plane uy the vertical plane

Bending field

- Circular accelerators deflecting forces are

needed - Circular accelerators piecewise circular orbits

with a defined bending radius ? - Straight sections are needed for e.g. particle

detectors - In circular arc sections the magnetic field must

provide the desired bending radius - For a constant particle energy we need a constant

B field ? dipole magnets with homogenous field - In a synchrotron, the bending radius,1/?eB/p, is

kept constant during acceleration (last section)

The reference trajectory

- An accelerator is designed around a reference

trajectory (also called design orbit in circular

accelerators) - This is the trajectory an ideal particle will

follow and consist of - a straight line where there is no bending field
- arc of circle inside the bending field
- We will in the following talk about transverse

deviations from this reference trajectory, and

especially about how to keep these deviations

small

Bending field dipole magnets

- Dipole magnets provide uniform field in the

desired region - LHC Dipole magnets design that allows opposite

and uniform field in both vacuum chambers - Bonus effect of dipole magnets geometrical

focusing in the horizontal plane - 1/? normalized dipole strength, strength of

the magnet

Focusing field

- reference trajectory typically centre of the

dipole magnets - Problem with geometrical focusing still large

oscillations and NO focusing in the vertical

plane ? the smallest disturbance (like

gravity...) may lead to lost particle - Desired a restoring force of the type Fx,y-kx,y

in order to keep the particles close to the ideal

orbit - A linear field in both planes can be derived from

the scalar pot. V(x,y) gxy - Equipotential lines at xyVconst
- B ? magnet iron surface
- ? Magnet surfaces shaped as hyperbolas gives

linear field

Focusing field quadrupoles

- Quadrupole magnets gives linear field in x and y
- Bx -gy
- By -gx
- However, forces are focusing in one plane and

defocusing in the orthogonal plane - Fx -qvgx (focusing)
- Fy qvgy (defocusing)
- Opposite focusing/defocusing is achieved by

rotating the quadrupole 90? - Analogy to dipole strength normalized quadrupole

strength

inevitable due to Maxwell

Optics analogy

- Physical analogy quadrupoles ? optics
- Focal length of a quadrupole 1/f kl
- where l is the length of the quadrupole
- Alternating focusing and defocusing lenses will

together give total focusing effect in both

planes (shown later) - Alternating Gradient focusing

The Lattice

- An accelerator is composed of bending magnets,

focusing magnets and non-linear magnets (later) - The ensemble of magnets in the accelerator

constitutes the accelerator lattice

Example lattice components

Transverse beam size

- RMS beam size

Lattice

Beam quality

Conclusion transverse dynamics

- We have now studied the transverse optics of a

circular accelerator and we have had a look at

the optics elements, - the dipole for bending
- the quadrupole for focusing
- the sextupole for chromaticity correction
- All optic elements ( more) are needed in a high

performance accelerator, like the LHC

Synchrotron radiation

Part 5

1) Synchrotron radiation

- Charged particles undergoing acceleration emit

electromagnetic radiation - Main limitation for circular electron machines
- RF power consumption becomes too high
- The main limitation factor for LEP...
- ...the main reason for building LHC !
- However, synchrotron radiations is also useful

(see later slides)

Show RAD2D here

- (anim)

Characteristic of SR power

Characteristics of SR distribution

- Electron rest-frame radiation distributed as a

"Hertz-dipole" - Relativist electron Hertz-dipole distribution in

the electron rest-frame, but transformed into the

laboratory frame the radiation form a very

sharply peaked light-cone

Characteristics of SR spectrum

- Broad spectra (due to short pulses as seen by an

observer) - But, 50 of power contained within a well defined

"critical frequency" - Summary advantages of Synchrotron Radiation
- Very high intensity
- Spectrum that cannot be covered easy with other

sources - Critical frequency easily controlled

Typical SR centre

Example European Synchrotron Radiation Facility

(ESRF), Grenoble, France

Accelerator Users

- Some applications of Synchrotron Radiation
- material/molecule analysis (UV, X-ray)
- crystallography
- archaeology...

Case LHC

LHC

LHC injector system

- LHC is responsible for accelerating protons from

450 GeV up to 7000 GeV - 450 GeV protons injected into LHC from the SPS
- PS injects into the SPS
- LINACS injects into the PS
- The protons are generated by a Duoplasmatron

Proton Source

LHC layout

- circumference 26658.9 m
- 8 interaction points, 4 of which contains

detectors where the beams intersect - 8 straight sections, containing the IPs, around

530 m long - 8 arcs with a regular lattice structure,

containing 23 arc cells - Each arc cell has a FODO structure, 106.9 m long

LHC beam transverse size

beta in drift space b(s) b (s-s)2 / b

LHC cavities

- Superconducting RF cavities (standing wave, 400

MHz) - Each beam one cryostats with 44 cavities each
- Located at LHC point 4

LHC main parametersat collision energy

References

- Bibliography
- K. Wille, The Physics of Particle Accelerators,

2000 - ...and the classic E. D. Courant and H. S.

Snyder, "Theory of the Alternating-Gradient

Synchrotron", 1957 - CAS 1992, Fifth General Accelerator Physics

Course, Proceedings, 7-18 September 1992 - LHC Design Report online
- Other references
- USPAS resource site, A. Chao, USPAS january 2007
- CAS 2005, Proceedings (in-print), J. Le Duff, B,

Holzer et al. - O. Brüning CERN student summer lectures
- N. Pichoff Transverse Beam Dynamics in

Accelerators, JUAS January 2004 - U. Amaldi, presentation on Hadron therapy at CERN

2006 - Several figures in this presentation have been

borrowed from the above references, thanks to all!